When I pull up plastic mulch there is often worms right under it. This means even it does not prevent them from being on a site, but it does interfere with gaseous exchange - so they are against the plastic, instead of deeper in the soil where they would be otherwise. In your situation I would get rid of the plastic and then replace the organic mulch. Bark would be better than compost because of the larger particle size making it a more effective barrier. Otherwise the preferred mulch, where there are not a lot of small plants that might get smothered is free wood chips from a tree service - as long as these don't come with trash or weeds like giant morning glory. To be sure of clean material cedar play chips can be purchased from a bark and soil dealer, when and where available.

You can buy worms or pick them from other location and drop them in there. Worms love tree leaves . I would bury a lot of leaves in the bed . With the clay you would need A LOT of compost/organic material.
Just throw the worms in wet well cultivated ground. They will find their way around. They are NOT going to stay where you place them, anyway. If your garden/flower bed has enough organic matter and it is not poisoned by some weed/insects killer, They will multiply sooner than you think, But you have to keep adding and tilling in compost, leaves..

Most worms that can be purchased will die when added to a garden.

Instead, incorporate lots of compost & the existing worms will multiply.

I'd just put it on top of the soil, like nature does.

Thanks for all the suggestions.

There are no worms there right now.

You need to get rid of the plastic. I had an area of yard with inches of bark mulch over plastic. No worms in the bark mulch but plenty of weeds. When I pulled up the plastic, the dirt seemed hard and clayey. Now, after a few years there are plenty of worms and the soil is not so packed down.